1. Field of the Invention
This invention relates to seismic exploration and more particularly, to a method for correctly restoring seismic traces using F-K filtering. This invention further relates to a method for restoring coherent events to missing traces in seismic data.
2. Description of the Prior Art
In seismic exploration, it is common practice to deploy a large array of geophones on the surface of the earth and to record the vibrations of the earth at each geophone location to obtain a collection of seismic traces. The traces are sampled and recorded for further processing. When the vibrations so recorded are caused by a seismic source activated at a known time and location, the recorded data can be processed by a computer in known ways to produce an image of the subsurface. The image thus produced is commonly interpreted by geophysicists to detect the possible presence of valuable hydrocarbons.
Seismograms are commonly recorded as digital samples representing the amplitude of a received seismic signal as a function of time. Since seismograms are usually obtained along a line of exploration on the surface of the earth, the digital samples can be formed into x-t arrays with each sample in the array representing the amplitude of the seismic signal as a function of horizontal distance and time. When such arrays are visually reproduced, by plotting or the like, seismic sections are produced. A seismic section depicts the subsurface layering of a section of the earth. It is the principal tool which the geophysicists studies to determine the nature of the earth's subsurface formations. Before an array of seismic samples or traces can be converted into a seismic section for interpretation by geophysicists, the array must be extensively processed to remove noise and to make reflection events discernible.
In the processing of seismograms, x-t arrays are sometimes transformed into arrays representing amplitude as a function of frequency and wave number. This is commonly referred to as a "frequency-wave number" or "f-k" transformation. The f-k transformation has been used as a tool to study seismic filtering. F-k transforms are routinely used to represent data collected by large arrays of sensors, including seismic data. Usually, the f-k representations are computed by Fast Fourier Transforms (hereafter referred to as FFTs). The resulting data representations are parameterized by frequencies, wave numbers (spatial frequencies), amplitudes, and phases. In particular, for each frequency there is a collection of wave numbers, and for each frequency-wave number pair there is a complex number representative of an amplitude and a phase. Among various applications of this representation are spectrum analysis (displaying the amplitude squared as a function of frequency and wave number) and filtering in the frequency-wave number domain.
In U.S. Pat. No. 4,218,765 issued to Kinkade, seismic traces are transformed to an f-k array and filtering is performed on the traces in the f-k domain. In U.S. Pat. No. 4,380,059 issued to Ruehle, multiple reflections are filtered from seismograms by transforming them into an f-k array representing amplitude as a function of frequency and wave number. In Ruehle, the f-k array of the seismograms is filtered by weighting all samples with the inverse of the f-k transform of the multiple reflections. In U.S. Pat. No. 4,594,693 issued to Pann et al, seismic trace interpolation is carried out by inserting zero amplitude traces between the seismic traces in a section where spatial aliasing is a problem. The traces are then transformed into an f-k array. The f-k array is filtered with a filter which rejects samples in a region of frequency and wave number which exhibits aliasing. The filtered f-k array is then transformed back into a seismic section representing amplitude as a function of time and distance.
A common problem during seismic data acquisition is the presence of seismic traces with no recorded data or seismic traces that clearly contain severe noise contamination. For example, the failure of one or more geophones intended to collect data can result in a seismic trace without data. Severe contamination, on the other hand, can result from numerous sources including random bursts of noise, multiple or intrabed reflections or ground roll.
Standard practice among geophysicists faced with seismic traces with no recorded data or severely contaminated seismic traces has been to exclude such traces, commonly referred to as "null" traces, from the otherwise satisfactory data set. The collected seismic data would be processed normally without the excluded data. When the missing trace was necessary for proper processing of the seismic data, prior attempts to restore the missing trace and create a trace with events consistent with nearby coherent events focused upon combining traces near the missing trace in the x-t domain to create the missing trace.
F-k spectrum analysis and filtering are particularly useful when seismic data are contaminated by large amplitude coherent noise which obscures geologically significant signals. Frequently, the coherent noise is concentrated in a different part of the f-k spectrum than the signals. In such cases, f-k filtering can potentially be used to attenuate the coherent noise and thus reveal the seismic signals for interpretation. However, the f-k filtering of seismic data to remove coherent noise does not produce satisfactory results when null traces interrupt large amplitude coherent events which are to be filtered out using an f-k filter discriminating primarily on dip. In these situations, significant processing noise is generated. This processing noise contaminates the filtered data trace corresponding to the previously missing trace and sometimes several adjacent traces. The processing noise thus generated potentially interferes with prestack interpretation and other processing.